Estimating a predator-prey dynamical model with the parameter cascades method

Biometrics

Volumn 64, Issue 3, 2008, Pages 959-967

  Cao, Jiguo ^a   Fussmann, Gregor F ^b   Ramsay, James O ^b  

^a SIMON FRASER UNIVERSITY   (Canada)

^b MCGILL UNIVERSITY   (Canada)

Author keywords

Inverse problem; Nuisance parameters; Ordinary differential equation; Penalized smoothing; Predator prey system; Profiling method; System identification

Indexed keywords

ECOSYSTEMS; ORDINARY DIFFERENTIAL EQUATIONS; PARAMETER ESTIMATION; PARAMETERIZATION; PREDATOR PREY SYSTEMS; UNCERTAINTY ANALYSIS;

DYNAMICAL MODELING; EQUATION PARAMETER; FUNCTIONAL RESPONSE; NUISANCE PARAMETER; ORDINARY DIFFERENTIAL EQUATION MODELS; PENALIZED SMOOTHING; PREDATOR - PREY SYSTEM; PREDATOR-PREY; PROFILING METHODS; SYSTEM-IDENTIFICATION;

INVERSE PROBLEMS;

DATA SET; ECOLOGICAL MODELING; ESTIMATION METHOD; EXPERIMENTAL STUDY; FUNCTIONAL RESPONSE; INVERSE PROBLEM; MODEL VALIDATION; NUMERICAL MODEL; PARAMETERIZATION; PREDATOR-PREY INTERACTION; SMOOTHING;

ACCURACY; ARTICLE; ECOLOGY; MATHEMATICAL MODEL; MATHEMATICAL PARAMETERS; NOISE; PREDATOR PREY INTERACTION; VALIDATION STUDY;

EID: 49749099233     PISSN: 0006341X     EISSN: 15410420     Source Type: Journal    
DOI: 10.1111/j.1541-0420.2007.00942.x     Document Type: Article

References (30)

1. Becks, L., Hilker, F. M., Malchow, H., Jürgens, K., and Arndt, H. (2005). Experimental demonstration of chaos in a microbial food web. Nature 435, 1226.
2. Bock, H. G. (1983). Recent advances in parameter identification techniques for ordinary differential equations. In Numerical Treatment of Inverse Problems in Differential and Integral Equations, P. Deuflhard and E. Harrier (eds 95 121. Basel, Switzerland : Birkhäuser.
3. Cao, J. and Ramsay, J. O. (2007). Parameter cascades and profiling in functional data analysis. Computational Statistics 22, 335 351.
4. de Boor, C. and Swartz, B. (1973). Collocation at Gaussian points. SIAM Journal on Numerical Analysis 10, 582 606.
5. Ellner, S. P., Kendall, B. E., Wood, S. N., McCauley, E., and Briggs, C. J. (1997). Inferring mechanism from time-series data: Delay-differential equations. Physics D 110, 182 194.
6. Ellner, S. P., Seifu, Y., and Smith, R. H. (2002). Fitting population dynamic models to time-series data by gradient matching. Ecology 83, 2256 2270.
7. Fussmann, G. F. and Blasius, B. (2005). Community response to enrichment is highly sensitive to model structure. Biology Letters 1, 9 12.
8. Fussmann, G. F., Ellner, S. P., Shertzer, K. W., and Hairston, N. G. J. (2000). Crossing the Hopf bifurcation in a live predator-prey system. Science 290, 1358 1360.
9. Fussmann, G. F., Ellner, S. P., Hairston, N. G., Jones, L. E., Shertzer, K. W., and Yoshida, T. (2005). Ecological and evolutionary dynamics of experimental plankton communities. Advances in Ecological Research 37, 221 243.
10. Fussmann, G. F., Weithoff, G., and Yoshida, T. (2005). A direct, experimental test of resource vs. consumer dependence. Ecology 86, 2924 2930.
11. Gelman, A., Bois, F., and Jiang, J. (1996). Physiological pharmacokinetic analysis using population modeling and informative prior distributions. Journal of the American Statistical Association 91, 1400 1412.
12. Hassell, M. P., Lawton, J. H., and Beddington, J. R. (1977). Sigmoid functional responses by invertebrate predators and parasitoids. Journal of Animal Ecology 46, 249 262.
13. Himmelblau, D., Jones, C., and Bischoff, K. B. (1967). Determination of rate constants for complex kinetics models. Industrial Engineering Chemistry Fundamentals 6, 539.
14. Holling, C. S. (1959). The components of predation as revealed by a study of small-mammal predation of the European pine sawfly. The Canadian Entomologist 91, 293 320.
15. Ionides, E. L., Breto, C., and King, A. A. (2006). Inference for nonlinear dynamical systems. Proceedings of the National Academy of Sciences 103, 18438 18443.
16. Ivlev, V. S. (1961). Experimental Ecology of the Feeding of Fishes. New Haven, CT : Yale University Press.
17. Jensen, C. X. J., Jeschke, J. M., and Ginzburg, L. R. (2007). A direct, experimental test of resource vs. consumer dependence: Comment. Ecology 88, 1600 1602.
18. Jost, C. and Ellner, S. P. (2000). Testing for predator dependence in predator-prey dynamics: A non-parametric approach. Proceedings of the Royal Society of London, Series B - Biological Sciences 267, 1611 1620.
19. Kendall, B. E., Briggs, C. J., Murdoch, W. W., Turchin, P., Ellner, S. P., McCauley, E., Nisbet, R. M., and Wood, S. N. (1999). Why do populations cycle? A synthesis of statistical and mechanistic modeling approaches. Ecology 80, 1789 1805.
20. Kondoh, M. (2003). Foraging adaptation and the relationship between food-web complexity and stability. Science 299, 1388 1391.
21. Murdoch, W., Briggs, C., and Nisbet, R. (2003). Consumer-Resource Dynamics. New York : Princeton University Press.
22. Ramsay, J. O. and Silverman, B. W. (2005). Functional Data Analysis, 2nd ed. New York : Springer.
23. Ramsay, J. O., Hooker, G., Campbell, D., and Cao, J. (2007). Parameter estimation for differential equations: A generalized smoothing approach (with discussion). Journal of the Royal Statistical Society, Series B 69, 741 746.
24. Rosenzweig, M. L. and MacArthur, R. H. (1963). Graphical representation and stability conditions of predator-prey interactions. American Naturalist 97, 209.
25. Shertzer, K. W., Ellner, S. P., Fussmann, G. F., and Hairston, N. G. (2002). Predator-prey cycles in an aquatic microcosm: Testing hypotheses of mechanism. Journal of Animal Ecology 71, 802 815.
26. Turchin, P. (2003). Complex Population Dynamics. Princeton, NJ : Princeton University Press.
27. Vos, M., Kooi, B. W., DeAngelis, D. L., and Mooij, W. M. (2004). Inducible defences and the paradox of enrichment. Oikos 105, 471 480.
28. Williams, R. J. and Martinez, N. D. (2004). Stabilization of chaotic and non-permanent food-web dynamics. European Physical Journal B 38, 297 303.
29. Wood, S. N. (2001). Partially specified ecological models. Ecological Monographs 71, 1 25.
30. Yoshida, T., Jones, L. E., Ellner, S. P., Fussmann, G. F., and Hairston, N. G. (2003). Rapid evolution drives ecological dynamics in a predator-prey system. Nature 424, 303 306.